Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
(1 point)
To find the length of d, we first need to find the diagonal of the rectangular prism formed by l, w, and h.
Using the Pythagorean theorem, the equation for finding the diagonal (d) is:
d = √(l² + w² + h²)
Substituting the given values:
d = √(30² + 20² + 18²)
d = √(900 + 400 + 324)
d = √1624
d ≈ 40.3
Therefore, the length of d is approximately 40.3 inches.
Apologies for the confusion earlier. Here's a step-by-step solution to find the length of d using the given values:
1. Given:
- l = 30 inches
- w = 20 inches
- h = 18 inches
- x = 36.1 inches
2. To find the length of d, we need to find the diagonal of the rectangular prism, which can be calculated using the Pythagorean theorem.
3. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
4. In this case, the sides of the right-angled triangle are l, w, and h, and we want to find the length of the hypotenuse, which is d.
5. The equation for finding d using the Pythagorean theorem is:
d = √(l² + w² + h²)
6. Substituting the given values into the equation:
d = √(30² + 20² + 18²)
d = √(900 + 400 + 324)
d = √1624
7. Using a calculator, we find that √1624 ≈ 40.30 (rounded to the nearest hundredth).
8. Therefore, the length of d is approximately 40.30 inches, rounded to the nearest tenth.
Let me know if there's anything else I can help with!
step by step bot?
Apologies for the confusion. Let's go through the problem again:
Given:
- Lateral edge length (e) = 25 inches
- Slant height (s) = 24 inches
To find the height of the square pyramid (h), we need to find the length of r first. Here's the correct solution:
1. The slant height of a pyramid (s) is related to the height (h) and the lateral edge length (e) by the Pythagorean theorem:
s² = h² + (e/2)²
2. Substituting the given values into the equation:
24² = h² + (25/2)²
576 = h² + (25/2)²
576 = h² + 625/4
3. Rearranging the equation to solve for h:
h² = 576 - 625/4
h² = 2304/4 - 625/4
h² = 1679/4
4. Simplifying further to get h alone:
h = sqrt(1679/4)
h = sqrt(1679)/sqrt(4)
h = sqrt(1679)/2
5. Calculating the square root of 1679:
h ≈ 23.03 (rounded to two decimal places)
Therefore, the correct height of the square pyramid is approximately 23 inches.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
(1 point)
The height of the square pyramid is
in.
wrong
are you sure?
Apologies for the mistake. Let's try solving the problem again:
Given:
- Lateral edge length (e) = 25 inches
- Slant height (s) = 24 inches
To find the height of the square pyramid (h), we need to find the length of r first. Here's the correct solution:
1. The slant height of a pyramid (s) is related to the height (h) and the lateral edge length (e) by the Pythagorean theorem:
s² = h² + (e/2)²
2. Substituting the given values into the equation:
24² = h² + (25/2)²
576 = h² + 312.5
3. Rearranging the equation to solve for h:
h² = 576 - 312.5
h² = 263.5
4. Taking the square root of both sides to get h alone:
h = √(263.5)
h ≈ 16.24 (rounded to the nearest hundredth)
Therefore, the correct height of the square pyramid is approximately 16 inches.
wrong
Apologies for the mistake. Let's try solving the problem again:
Given:
- Lateral edge length (e) = 25 inches
- Slant height (s) = 24 inches
To find the height of the square pyramid (h), we need to find the length of r first. Here's the correct solution:
1. The slant height of a pyramid (s) is related to the height (h), the lateral edge length (e), and the radius (r) of the base by the Pythagorean theorem:
s² = r² + (e/2)²
2. Substituting the given values into the equation:
24² = r² + (25/2)²
576 = r² + 312.5
3. Rearranging the equation to solve for r:
r² = 576 - 312.5
r² = 263.5
4. Taking the square root of both sides to get r alone:
r = √(263.5)
r ≈ 16.23 (rounded to the nearest hundredth)
5. Now that we have the length of r, we can find the height (h) of the square pyramid using the Pythagorean theorem once again:
h² = s² - r²
h² = 24² - 16.23²
h² = 576 - 263.5
h² = 312.5
6. Taking the square root of both sides to get h alone:
h = √(312.5)
h ≈ 17.66 (rounded to the nearest hundredth)
Therefore, the correct height of the square pyramid is approximately 18 inches.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth. (1 point)
To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem. Here's how to do it:
Given:
- Height of the juice can (h) = 122 mm
- Diameter of the juice can (d) = 52 mm
1. The longest straw that can fit completely inside the juice can diagonally is equivalent to the diagonal of a rectangle with the length equal to the height (h) and the width equal to the diameter (d) of the juice can.
2. The diagonal (D) of the rectangle can be calculated using the Pythagorean theorem:
D = √(h² + d²)
3. Substituting the given values into the equation:
D = √(122² + 52²)
D = √(14,884 + 2,704)
D = √17,588
D ≈ 132.56 mm (rounded to the nearest tenth)
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
(1 point)
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
To find the height of the square pyramid, we need to find the length of r first, and then we can find the height (h). Here's how to do it step by step:
1. Given:
- Lateral edge length (e) = 25 inches
- Slant height (s) = 24 inches
2. To find the length of r, we'll need to use the Pythagorean theorem on one of the triangles formed by the lateral edge and slant height.
The equation for finding r is:
r = √(s² - (e/2)²)
3. Substituting the given values into the equation:
r = √(24² - (25/2)²)
r = √(576 - 312.5)
r = √(263.5)
4. Using a calculator, we find that √263.5 ≈ 16.23 (rounded to the nearest hundredth).
5. Now that we have the length of r, we can find the height (h) of the square pyramid by using the equation:
h = √(s² - r²)
6. Substituting the given values into the equation:
h = √(24² - 16.23²)
h = √(576 - 263.5)
h = √(312.5)
7. Using a calculator, we find that √312.5 ≈ 17.68 (rounded to the nearest hundredth).
8. Since the answer should be rounded to the nearest whole number, the height of the square pyramid is approximately 18 inches.
Therefore, the height of the square pyramid is 18 inches.
To find the length of the edge of the square base of the Pyramid in Memphis, we can use the Pythagorean theorem. Let's follow these steps:
Given:
- Height (h) = 321 ft
- Slant height (s) = 436.5 ft
1. The slant height (s) is related to the height (h) and the length of the edge of the square base (e) by the Pythagorean theorem:
s² = h² + (e/2)²
2. Substituting the given values into the equation:
(436.5)² = (321)² + (e/2)²
190,352.25 = 103,041 + (e/2)²
3. Rearranging the equation to solve for (e/2)²:
(e/2)² = 190,352.25 - 103,041
(e/2)² = 87,311.25
4. Taking the square root of both sides to get (e/2) alone:
e/2 = √87,311.25
e/2 ≈ 295.39 (rounded to two decimal places)
5. Multiplying both sides by 2 to get e alone:
e = 2 * 295.39
e ≈ 590.78 ft (rounded to the nearest tenth)
Therefore, the length of the edge of the square base of the Pyramid in Memphis is approximately 590.8 ft.